Book Image

Applying Math with Python

By : Sam Morley
Book Image

Applying Math with Python

By: Sam Morley

Overview of this book

Python, one of the world's most popular programming languages, has a number of powerful packages to help you tackle complex mathematical problems in a simple and efficient way. These core capabilities help programmers pave the way for building exciting applications in various domains, such as machine learning and data science, using knowledge in the computational mathematics domain. The book teaches you how to solve problems faced in a wide variety of mathematical fields, including calculus, probability, statistics and data science, graph theory, optimization, and geometry. You'll start by developing core skills and learning about packages covered in Python’s scientific stack, including NumPy, SciPy, and Matplotlib. As you advance, you'll get to grips with more advanced topics of calculus, probability, and networks (graph theory). After you gain a solid understanding of these topics, you'll discover Python's applications in data science and statistics, forecasting, geometry, and optimization. The final chapters will take you through a collection of miscellaneous problems, including working with specific data formats and accelerating code. By the end of this book, you'll have an arsenal of practical coding solutions that can be used and modified to solve a wide range of practical problems in computational mathematics and data science.
Table of Contents (12 chapters)

Integrating functions numerically using SciPy

Integration can be interpreted as the area that lies between a curve and the xaxis, signed according to whether this area is above or below the axis. Some integrals cannot be computed directly, using symbolic means, and instead have to be approximated numerically. One classic example of this is the Gaussian error function, which was mentioned in the Basic mathematical functions section in Chapter1, Basic Packages, Functions, and Concepts. This is defined by the formula

and the integral that appears here cannot be evaluated symbolically.

In this recipe, we will see how to use the numerical integration routines in the SciPy package to compute the integral of a function.

Getting ready

We use the scipy.integratemodule, which contains several routines for computing numerical integrals. We import this module as follows:

from scipy import integrate

How to...